What the bleep is going on in tai chi's single whip posture? It seems to be emblematic of tai chi, being a pose frequently struck by practitioners in the presence of cameras.

The actual sequence is shown in this short video clip. Coming from an outsider's perspective, this looks like a tough position to apply in a fighting context. What is the martial application of this sequence or posture?

That looks more like a Diagonal Flying application to me, though I see how it could be applied to Single Whip. 1:20-1:30 of your video is definitely Single Whip, though.
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Dave LiepmannMay 29 '12 at 15:53

5 Answers
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One application is to capture a punch. If you enter the puncher's space, there's an arm break and/or a relatively violent takedown similar to some silat takedowns.

It can be a deflection and striking/throwing entry without any capturing or breaks.

One application

Attacker steps in with a right-hand punch. Defender outward-deflects punch using the right arm and hooks over top of the attacker's arm. (This can be enough to temporarily capture the arm, it can be a grab, etc.)

Defender steps in and brings left arm across attacker's neck.

Arm break is sticking chest forward while bringing arms back (depending on alignment).

Takedown by dropping center, bending the left arm and sticking elbow into neck or shoulder depression makes it even easier, as does off-centering attacker backwards. Can be assisted with a hip nudge and/or knee to back of attacker's lead knee.

A more silat-ish application would have defender's left hand rise from under the attacker's punch; this can be an uppercut. It may also turn in to coming over the top of the attacker's neck, after which much merriment arises.

Could you go into some detail on one of those applications, perhaps describing it in stages?
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Dave LiepmannMay 24 '12 at 21:16

@DaveLiepmann I tried; I've never been particularly good at describing applications, though :)
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Dave NewtonMay 24 '12 at 21:28

Thanks! One point of confusion on my part--is the defender's right arm involved in any of that application?
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Dave LiepmannMay 24 '12 at 21:33

@DaveLiepmann The right arm is what does the initial deflection and capture. The arm break, for example, requires def. right arm to still have the attacker's right arm immobilized, otherwise there can't be a break.
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Dave NewtonMay 24 '12 at 21:40

There are many applications, depending on what part of the single whip sequence one looks at.

There is hooking and pull-down and push with the right hand at the beginning of the motion.

Then there is a potential albeit well hidden elbow strike when turning around.

Then there is a combination of a ward-off, pull-down and push, the end of which can be seen on the picture. These are just the "text book" applications the way I've learned the form. With enough practice and proper mind intent, the movements may reveal more subtler applications.

The important thing to realize here is that applications in the form are given only as a guide to understanding the intent of the movements in the form while learning it. The true work and insight will come from adding to the form everything one learns from push-hands exercises, swordplay and sanshou practices, to name a few.

I've studied Yang style Tai Chi for two years. There are some very simple applications for Single Whip:

In the images above, the guy is facing forwards, imagine if the attacker was coming from behind. You start in Wu Chi and when they try to punch the back of your head, you step backwards into single whip, using the whip hand to very subtly deflect the punch. very basic, very powerful.

The power of the movement comes from being a small shape and expanding into a larger shape that over laps the other person. Moving towards a punch is the important part.

The whip hand is also seen in 'Snake Creeps Down' (03:20 > https://www.youtube.com/watch?v=TBvF6r6DOvc) near the end, you could use the upwards pointing whip hand to grab a kicking leg and then move into single whip to lift the leg high enough to push someone over.

We're looking for long answers that provide some explanation and context. Don't just give a one-line answer; explain why your answer is right, ideally with citations. Answers that don't include explanations may be removed.

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Could you summarize the video here?
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Dave LiepmannJul 25 '13 at 21:19

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Alas, the summary is the title; I find it very difficult to summarize kinesthesiology in text. Essential Mr. Gilmer demonstrates a number of variations of single whip in response to attacks.
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Mark C. WallaceJul 28 '13 at 20:39

@DaveLiepmann If you ask me, trying to use single whip for anything except exploding force through the front palm is silly.
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sirdankJan 5 at 15:41

No, that little loopy thing you do with your hand as it curls into a crane's beak? That's a chin-na technique. It's to deal with a wrist grab. You are disengaging the grab and simultaneously grabbing his wrist and extending his arm out. This can be done from the inside or the outside position. On the inside position, the follow-up palm strike is to the face (stomach-5) or neck (stomach-9). On the outside position, the follow-up palm strike is actually a standing elbow lock/break and possible throw.
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Steve WeigandJan 10 at 23:46

@SteveWeigand Could you post that as an answer please?
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Dave LiepmannJan 23 at 17:26

Yeah, I'll see what I can do later on today. I learned that application from a direct student of Chen Qingzhou, fyi. I think it's the only one that really makes any sense martially speaking.
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Steve WeigandJan 23 at 17:56